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An Analytic Picture Of Neuron Oscillations, Int. J. Bifur. & Chaos

Excerpts: Current induced oscillations of a space clamped neuron action potential demonstrates a bifurcation scenario originally encapsulated by the four-dimensional Hodgkin-Huxley equations. These oscillations were subsequently described by the two-dimensional FitzHugh-Nagum Equations in close agreement with the Hodgkin-Huxley theory. It is shown that the FitzHugh-Nagumo equations can to close approximation be reduced to a generalized van der Pol oscillator externally driven by the current. The current functions as an external constant force driving the action potential. As a consequence approximate analytic expressions are derived which predict the bifurcation scenario, the amplitudes of the oscillations (...).